The present invention relates to a heat exchanger of the type having a plastic header sheet including a sleeve-like connection nozzle associated with each tube opening for insertion into each tube and an annular groove extending coaxially to the opening for receiving the tube end inserted therein. A heat exchanger of this type is disclosed in German Offenlegungsschrift No. 3,133,665. In the known arrangement, the connection nozzle is located on that side of the header sheet which faces the heat exchanger block. This has the consequence, however, that a great deal of space is required between the tube sheet and the fin block for the connection nozzles and, for strength reasons, the connection nozzle part located radially outside the tube must be made relatively thick. Furthermore, for reasons of injection-molding technology, the long projecting end of the connection nozzles is also unfavorable, since it does not allow the injection mold to be filled uniformly.